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The figure below represents a cone of height 12cm and base radius of 9cm from which a similar smaller cone is removed, leaving a conical...
(Solved)
The figure below represents a cone of height 12cm and base radius of 9cm from which a similar smaller cone is removed, leaving a conical hole of height 4cm.

a)Calculate:
i) The base radius of conical hole.
ii)The volume, in terms of π of the smaller cone that was removed.
b)i) Determine, slant height of the original cone
ii)Calculate, in terms of π the surface area of the remaining solid after the smaller cone is removed.
Date posted:
October 16, 2019
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Answers (1)
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In the figure below, the tangent ST meets chord VU produced at T. Chord SW passes through the centre O, of the circle and intersects...
(Solved)
In the figure below, the tangent ST meets chord VU produced at T. Chord SW passes through the centre O, of the circle and intersects chord VU at X. Line ST = 12cm and UT = 8cm.

a)Calculate the length of chord VU.
b)If WX = 3cm and VX : XU = 2 : 3, find SX.
Date posted:
October 16, 2019
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Answers (1)
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The velocity, v m/s of a particle after t seconds is given by v = t2 – 2t + 4.
a)i) Using the mid- coordinate rule...
(Solved)
The velocity, v m/s of a particle after t seconds is given by v = t2 – 2t + 4.
a)i) Using the mid- coordinate rule with six strips, estimate the distance covered by the particle between t = 1 and t =13 seconds.
ii) Find the exact distance the particle covered between t =1 and t = 13 seconds.
b)Calculate the percentage error arising from the estimate in (a) above.
Date posted:
October 12, 2019
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Answers (1)
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Point R divides line PQ externally in the ratio 4:3. The position vectors of P and Q are 2i + j – 3k and i...
(Solved)
Point R divides line PQ externally in the ratio 4:3. The position vectors of P and Q are 2i + j – 3k and i – 2j + k respectively. Find the position vector, of R.
Date posted:
October 12, 2019
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Answers (1)
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The probability of a team losing a game is 1/5. The team plays the game until it wins. Find the probability that the team wins...
(Solved)
The probability of a team losing a game is 1/5. The team plays the game until it wins. Find the probability that the team wins in the fourth round.
Date posted:
October 12, 2019
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Answers (1)
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The figure below represents a hollow cylinder. The internal and external radii are estimated to be 6cm and 8cm respectively, to the nearest whole number....
(Solved)
The figure below represents a hollow cylinder. The internal and external radii are estimated to be 6cm and 8cm respectively, to the nearest whole number. The height of the cylinder is exactly 14cm.

a)Determine the exact values for the internal and external radii which will give maximum volume of the material.
b)Calculate the maximum possible volume of the material
Date posted:
October 12, 2019
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Answers (1)
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The current price of a vehicle is ksh. 500,000. The value of the vehicle depreciates at a rate of 15% p.a for the first two...
(Solved)
The current price of a vehicle is ksh. 500,000. The value of the vehicle depreciates at a rate of 15% p.a for the first two years and at 20% p.a thereafter. Find the number of years it will take for its value to reduce to ksh. 147,968.
Date posted:
October 12, 2019
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Answers (1)
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The figure below shows a triangular prism ABCDEF
a)Draw the net of the prism
b)A fly walks from A to D along the diagonals of rectangular...
(Solved)
The figure below shows a triangular prism ABCDEF

a)Draw the net of the prism
b)A fly walks from A to D along the diagonals of rectangular faces:
i)On your net show the locus of the fly.
ii)Measure the distance covered by the fly, one way.
iii)The fly takes 15 seconds to reach D one way. Calculate its’ speed in, km/h.
Date posted:
October 12, 2019
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Answers (1)
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A bus left Mombasa at 7.45 am towards Nairobi at an average speed of 60km/h. A saloon car left Mombasa at 9.15 am on the...
(Solved)
A bus left Mombasa at 7.45 am towards Nairobi at an average speed of 60km/h. A saloon car left Mombasa at 9.15 am on the same day along the same road at an average of 120km/h. the distance between Mombasa and Nairobi is 360km.
a)Determine the time of day when the salon car overtook the bus.
b)Both vehicles contained towards Nairobi at their original speed. How long had the saloon car waited in Nairobi before the bus arrived.
Date posted:
October 12, 2019
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Answers (1)
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Water and alcohol are mixed in the ratio 1:4. If the density of water and alcohol are 1g/cm3 and 0.8g/cm3 respectively. Find the density of...
(Solved)
Water and alcohol are mixed in the ratio 1:4. If the density of water and alcohol are 1g/cm3 and 0.8g/cm3 respectively. Find the density of the mixture.
Date posted:
October 11, 2019
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Answers (1)
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Two fair dice one a regular tetrahedron (4 faces) and the other a cube are thrown. The scores are added together. show all possible outcomes.
a)Find...
(Solved)
Two fair dice one a regular tetrahedron (4 faces) and the other a cube are thrown. The scores are added together. show all possible outcomes.
a)Find the probability that:
i) The sum is 6.
ii) The sum is an odd number.
iii)The sum is 6 or 9.
b)If a player wins a game by throwing a sum of 6 or 9, draw a tree diagram and use it to find
probability that he wins at least once when the dice are thrown twice
Date posted:
October 9, 2019
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Answers (1)
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The above diagram represents a wooden prism. ABCD is a rectangle. Points E and F are directly below C and B respectively. M is the...
(Solved)

The above diagram represents a wooden prism. ABCD is a rectangle. Points E and F are directly below C and B respectively. M is the midpoint of CD. AB = 8cm, BC = 10cm and CE = 4.5cm.
a)The size of angle CDE.
b) Calculate:
i) Length of AC.
ii) The angle CAE makes with the plane ADEF.
c) Find the:
i) Length of MB.
ii) Angle CBM.
Date posted:
October 9, 2019
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Answers (1)
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Make P the subject of the formula XYP = QPX
(Solved)
Make P the subject of the formula XYP = QPX
Date posted:
October 9, 2019
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Answers (1)
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A straight line passes through points (8, -2) and (4, -4)
a)Write its equation in the form ax + by + c = 0 where a,...
(Solved)
A straight line passes through points (8, -2) and (4, -4)
a)Write its equation in the form ax + by + c = 0 where a, b and c are integers.
b)If the line in (a) above cuts the x axis at point P, determine the coordinates of P.
c)Another line which is perpendicular to the line in (a) above passes through point P and cuts the
Y axis at the point Q. Determine the co-ordinates of point Q.
d)Find the length of QP.
Date posted:
October 9, 2019
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Answers (1)
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A passenger noticed that he had forgotten his bag in a bus 12 minutes after the bus had left. To catch up with the bus,...
(Solved)
A passenger noticed that he had forgotten his bag in a bus 12 minutes after the bus had left. To catch up with the bus, he immediately took a taxi which travelled 95km/h. The bus maintained an average speed of 75km/h.
Determine:
a)The distance covered by the bus in 12 minutes.
b)The distance covered by the taxi to catch up with the bus.
Date posted:
October 9, 2019
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Answers (1)
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A seven sided figure has three of its angles equal to x and the other angles are (2x - 30), (x + 28), 3(x -...
(Solved)
A seven sided figure has three of its angles equal to x and the other angles are (2x - 30), (x + 28), 3(x - 4) and (126 -x). Find the value of x.
Date posted:
October 9, 2019
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Answers (1)
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Given that Cos A = 5/13 and Angle A is acute, find the value of 2tan A + 3 Sin A.
(Solved)
Given that Cos A = 5/13 and Angle A is acute, find the value of 2tan A + 3 Sin A.
Date posted:
October 9, 2019
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Answers (1)
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A point (-3, 2) is the image of a point (7,4) after a reflection. Find the mirror line.
(Solved)
A point (-3, 2) is the image of a point (7,4) after a reflection. Find the mirror line.
Date posted:
October 9, 2019
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Answers (1)
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In the figure below AB is parallel to DE. Find the value of x and y.
(Solved)
In the figure below AB is parallel to DE. Find the value of x and y.

Date posted:
October 9, 2019
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Answers (1)
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Complete the table below, for the function y =2x2 + 4x - 3.
(Solved)
a) Complete the table below, for the function y =2x2 + 4x - 3.

b) On the grid provided, draw the graph of y=2x2 + 4x - 3 for -4<= x<= 2 and use the graph to estimate the roots of the equation to 1 decimal place.
c) In order to solve graphically 2x2 + x – 5 = 0, a straight line must be drawn to intersect the curve y = 2x2 + 4x – 3. Determine the equation of the straight line and draw it, hence obtain the roots of the equation 2x2 + x - 5 = 0 to 1 decimal place.
Date posted:
October 8, 2019
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Answers (1)